The Sequential Empirical Process of a Random Walk in Random Scenery

Martin Wendler

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arXiv · 1410.0824

The Sequential Empirical Process of a Random Walk in Random Scenery

Martin Wendler

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Abstract

A random walk in random scenery $(Y_n)_{n\in\mathbb{N}}$ is given by $Y_n=ξ_{S_n}$ for a random walk $(S_n)_{n\in\mathbb{N}}$ and iid random variables $(ξ_n)_{n\in\mathbb{Z}}$. In this paper, we will show the weak convergence of the sequential empirical process, i.e. the centered and rescaled empirical distribution function. The limit process shows a new type of behavior, combining properties of the limit in the independent case (roughness of the paths) and in the long range dependent case (self-similarity).

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BibTeX RIS

Martin Wendler. 2015-11-19. The Sequential Empirical Process of a Random Walk in Random Scenery. https://arxiv.org/abs/1410.0824

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